Balancing machine



' Sept. 21,l 1948. N; MINORSKY BALANCING MACHINE 2 Sheets-Sheet 1 Filed `May 4, 1943 Sept. 2l, 1948. N. MlNoRsKY 2,449,553

BALANCING MACHINE Filed May 4, 1943 2 Sheets-Sheet 2 NncoLm Nmcmm :lai/vv. J U 'l 'l q a. i

Patented Sept. 21, 1948 BALANCING MACHINE Nicolai Minorsky, Bethesda, Md., asslgnor to' Gyro-Balance Corporation, Greenwich. Conn., a corporation of Connecticut Application May 4, 1943, serial No. 485,656

3 claims. (c1. 29-1) This invention relates to improvements in balancing machines of' a type in which a continuous balancing procedure is guided by observations obtained by means responsive to the conditions of the 'prevailing unbalance.

More specifically the balancing machine forming the subject of this invention possesses the following characteristic advantages:

(a) Continuity of the balancing procedure without necessity of stopping the body to be balanced,

referred to in the following as the rotor, for the' purpose of adjusting the balancing weights;

(b) Independence `oi the balancing operation of the speed of the rotor;

(c) Independence of said operation of the parasitic phase angle, which complicates the balancing operation in the existing balancing machines.

The iirst mentioned advantage (a) derives from the fact that a deceleration and subsequent acceleration of the rotor required for the adjustment of magnitude and of angular position of balancing weight on the rotor during its stoppage, require generally a considerable time particularly for very high speed rotors, such as modern gyroscopes which results in a loss of time and hence in a decreased eiliciency of the balancing work.

The second mentioned advantage (b) is also important insofar as the existing balancing methods and machines become less reliable if the speed at which the balancing operation is performed is increased. This is the main reason why the existing balancing practice consists in balancing rotors normally intended to operate at a very high speed, at a considerably lower speed at which the existing methods and apparatus give satisfactory results. The drawback of this last mentioned procedure lies in the fact that a relatively satisfactory state of balance obtained at a lower speed may be entirely unsatisfactory at the normal high speed at which no efficient balancing can be obtained by the existing methods. The present invention permits of performing the balancing operation at any speed however high.

The third mentioned advantage (c) can be explained as follows. In the existing balancing machines based on the instantaneous observation of a certain characteristic condition of the rotor isolated from other preceding or following conditions by suitable means such as a flash of a stroboscopic light or other, it is generally assumed that the observed condition, such as deflection of a certain member compressing for instance a piezo-electric element or other pressure registering means, is in phase with the rotating unbalance force which it i-s desired to determine angularly at this instant. Such assumption is, generally, approximately correct and valid only for relatively small speeds owing to the existence of the so-called parasitic phase angle due partially to electrical causes, for instance such as the presence of electric filters in the circuit, and partially to mechanical causes due to exceedingly complicated and unpredictable effects of inertia, damping, molecular effects in the oil films in bearings, gyroscopic action and the like. While the electrical component of the parasitic phase angle can be determined and vcompensated for by suitable electrical means, such as phase shifting circuits and the like, the mechanical component of said angle remains totally unknown and unpredictable and therefore accounts for a lack of reliability of the balancing procedure particularly at higher speed-s at which its effects are increased. According to this invention the balancing procedure is made entirely independent of said undesirable e'ects of said parasitic phase angles as will be explained in the following.

In order to attain these three basic advantages in addition to a number of others which will be specied below, I provide a method and means for producing the balancing forces` and balancing couples with respect to the rotating axes of reference which are fixed with respect to the rotor. Since the unbalance forces and unbalance couples are also fixed with respect to said system of 'reierence, I am able to obtain in this manner a, condition of compensation of said last mentioned unbalance forces and couples by said first mentioned balancing forces and couples while the body is rotating, without any necessity for stopping it.

In order to be able to guide the balancing oper-` ation produced with respect to said rotating axes, or otherwise expressed, with respect to the rotating frame of reference, I provide means responsive to the prevailing state of unbalance on both bearings simultaneously, said responsive means being operatively associated with suitable indicating means exhibiting said conditions of the prevailing unbalance in the form of a luminous curve observed on a screen of a cathode ray oscillograph or an equivalent device.

The balancing procedure according to this invention consists in controlling the variation of balancing forces and balancing couples both in magnitude and in direction in response to corresponding variation of the shape, size, and orientation of said luminous curve in accordance with the method specified in the following.

From this preliminary disclosure of the 'broad features of this present invention the above stated fundamental advantages (a), (b), (c) become apparent.

In fact, said feature (a) becomes apparent because owing to the method and means of producing and controlling the magnitude and direction of balancing forces and balancing couples with respect to the rotating frame of'reference in which the original unbalance forces and couples also remain fixed, there is no necessity for stopping the rotor for subsequent adjustments so that the balancing operation is continuous in the above defined sense.

The second feature (b) is also* apparent because both the balancing operation and the indicating means which guide it towards 'the obtaining of a perfect balance, being individually independent of the speed, the balancing procedure as a whole does not depend on the speed either.

The third mentioned feature (c) becomes clear owing to the fact that the balancing operation according to this invention is conducted in response to the state of unbalance existing at both bearings simultaneously. The effect of the parasitic phase `angles referred to above cancel therefore in the combined response of both bearings, said response being represented by a luminous curve on the screen which guides the balancing procedure.

A number of additional advantages of this invention will become apparent from the following vdescription accompanied by drawings in which one embodiment of the invention is illustrated by way of example.

In the drawings,

Figure 1 shows diagrammatically in side elevation the balancing machine with the block diagram of electric circuits and the cathode ray oscillograph shown substantially in perspective;

Figure 2 is a view in side elevation showing a detail of the rotor shown in Figure 1 and the arrangement of the material removing tools;

Figure 3 is an end View of the rotor and the removing tools;

Figure 4 represents the vector diagram of rotating forces and their compensating components in the balancing planes;

Figure 5 is a diagram illustrating the method of balancing with respect -to the rotating axes;

Figures 6A, 7A, 8A, 9A, and 10A, and 10C, are diagrams showing the various forms of luminous curves observed on the screen of the cathode ray oscillograph for various conditions of balancing; and

Figures 6B, 7B, 8B, 9B, and 10B are diagrams showing the corresponding dynamical conditions giving rise to the occurrence of luminous curves shown in Figures 6A, 7A, 8A, 9A, 10A, and 10C respectively. y

Referring to Figure l, the reference numeral I indicates the piece to vbe balanced, which is designated in the followingv 'as the rotor, and has a` shaft I rotatably mounted in two bearings 2, 3, shown as the usual bearings employed for balancing. 'Ihe rotor I is driven by a motor P through -a coupling Q, and the whole device is supported on a -base L.

According to this invention the alternating component unbalance forces4 acting in the bearings along a fixed axis shown as a vertical axis AA (A'A) are transformed into electrical voltages suitably combined into a resultant response characterizing the state of the prevailing unbalance which is eliminated by means hereinafter described. i

shown. Supporting means of similar construction are shown and described in application Serial No. 266,714 of Rouy filed April 7, 1939, now Patent No. 2,329,654, granted September 14, 1943.

It is to be understood that the pressure responsive scheme does not form the subject of this invention and for that reason isdescribed with a minimum of details. Instead of a quartz system, I can use any other well known similar system such as a magnetostriction pressure responsive system, carbon-pile elements, or the like.

In the following, however, a piezo-electric quartz system is described as a preferred embodiment of this invention particularly suited for a high speed balancing.

The alternating potentials generated in quartz crystals 4, I5, in response to the alternating vertical components of unbalance forces, are applied by means uf condensers 8, 9, substantially as shown, to the input terminals I0, II of the grids of two vacuum tube amplifiers I2, I3.

The numerals I5 and I6 designate output terminals of the plates of the vacuum tube amplifiers, connected to resistors I1 and I8 and through them to the positive terminal I9 of B supply source, not shown. Resistors I1 and I8 are preferably supplied with attenuators indicated by other connection well known in the art can be.

also employed for the purpose specified below. The operation of this part of the system is apparent. The voltages impressed on the grids of tubes I2 and I3, in view of what has been previously explained, represent in magnitude and phase the dynamic reactions received by the piezo crystals. If tubes I2 and I3 are adjusted to function on their substantially rectilinear parts of (Vg, Ip) characteristics, the plate current variations are also representative of these reactions, both in magnitude and phase, and so are the potential drops in the plate resistors I1 and I8. In view of these connections, the electric field on 23, 23' on the one hand, and 24. 24' on the other,are proportional to the chmic drops across resistors I1 and I8, hence to the current variations and to Eg of I2 and Eg cf I3 and therefore to the dynamic reactions, which they represent both in magnitude and phase. This results in the Lissajou curves on the screen hereinafter described.

The adjustment of the magnitude of the oscillation (individually or jointly) along the an: and the yy axes is accomplished by means of the sliding contacts 20, 2|.

The cathode ray tube is of an ordinary comrby dotted lines.

3|', 32', situated in planes a', b', c', d is locatedv atrasos 4 mercial .type comprising, in addition to said de- However, there is shown in lpreviously described;` 'numerals' relative to the From this description it fouows that if an:

alternating vertical force is applied to crystal 4, and no force is applied to crystal 6, the luminous spot on thescreen 28 will oscillate along the horizontal straight line shown as the :c axis, indicated in perspective on screen 28; if, however, an alter--` nating force is applied to crystal 5 and no force is applied to crystal 4, the luminous spotv on the base. l

movingA tools 33,34, 33, ,33. All four removingA same parts are the same in Figures 1 and 2, or

.which the latter represents a part oi the Vformer confined to rotor I. Figure 3 shows the axial; view of the rotor shown in Figure 2. Referring to Figures 2and 3, 4| is a rod supported by pedestais4 34, 55, shown as fastened to the base plate t R. on which` the balancing, machine is mounted: however, in order to avoid the vibrations, the pedestals 34 and 33 maybe mounted on a separate On the rod 4|-,are rotatably mounted retools are videntical so that it is suilicient' topdescribeone of themfforexample tool 33 which is shown also in Figure 3. iThe tool consists of an e arc`shapedmember, the upper'and lower portions screen will be seen as a brightsegment along the y axis. The said axes :n andy on the screenl will be referred to below as theprincipal axes of the screen 28. From the above description it oi lwhich are offset as'shown in Figure 2 so' as to coincide with planes a,` b, at'right angles to the follows that the motion of the luminous spot on the screen along the principal axis :c is caused by an alternating unbalance force applied to bearing 2 and the corresponding motion of saidspot along.

the principal axis y is caused by a similar force appearing in bearing 3. Y

According to this invention the balancing op-J' eration is performed by removing a certain amount of material from balancing weights suit-v ably positioned on the surfaceof rotor or otherwise located in relation thereto. These balancing axis of rotation oi' the rotor. Atthe ends of the arc shaped memberthere aretwo holders 31 and 33 which hold suitableabrasive materials shown as pieces 33, 43, in Figure 3, and which may be replaced by any other similarremoving tool.

" Hneutral position at which neither of abrasive 4materials 33,40 touches corresponding ,weights weights may be i'ornied by small amounts of a suitable. material Veither soldered or welded or g otherwise secured in aj'few predetermined places as explainedbelow. For a low speed balancing, the 'balancing weightsfmust b'e relatively large; however, for balancing at very high speed, these weights can be very small.'

Although 'this invention is applicable for both'` v low and high speed balancing, it fis particularly useful in connectionwith balancing at high speeds for which there Vexistlno practical methods of balancing at present.` `For these highv speeds of balancing, even a very slight change .in balancing weights accounts for very considerable changes 'in forceslappliedeto, bearings Vas will 'be shown.

30', 3|', 32' arelocated in eight balancing planes a, b, c, d, and 'at-b', c','d'., respectively,.as shown in Figure 1. The weights 23and 3 0 are contained in the same plane passing., through -theaxis of rotation Aof rotor but are locatedonopposite sides of it substantially as shown, the weight 23 being .The assembly of the removing toolV 33, for

example, is mounted on the rod 4| by means ci!l aihub 442 and normally can be maintained in 23, 33,l contained in planes a, b. This neutral position can be secured either by means of a friction between the hub 42 and the supporting rod 4| or by means of suitable springs not shown.

' Theltoolassemblies 33.34, 35, 33v can be slightly rotated one way or the other about this neutral position by'meansof suitable levers', of which lever; 43 shown in Figure 3 in connection` with `assembly 33 is an example.

`If lever 43 is moved upwards in the direction of the. arrow shown in Figure 3 the abrasive material 33 comes in contact with weight 33 rotating i in' plane b and begins to remove the material from it during `the rotation of the rotor; if lever 43 is moved downwards, the removal of material takes placefrom the Vweight 23 rotating in plane a. A similar operation can be obtained by means o! Y vother levers, associated with assemblies 34, 33, 33 The balancing weights 23', 33, 3|l 32, and 23,

, weights 32, 33', 32', for upward motion, or from 4,weights 3|, 23', 3|', for downward motion. of said l whereby the removal of weight either from levers, can beV obtained.

`:By manipulating the 'four levers attached to jthe material removingassemblies 33, 34 35. 33 A in the above describedA manner, it is possible to in the plane @perpendicular to the axisof rotation and the weight33 in the plane b parallel to the plane a. The balancingweights3l, 3 2 are located in thehsame axal .plfneat right angles to the first mentioned 'axial 'plane in which the weights 29 land'3ll are contained. Similarly the` weights 3| and 32 are on opposite'sides of the remove the material from balancing weights 23,

30, 3|, 32, 23', 33', 3|', 32', shown in Figure 1 either separately `or jointly depending whether lever is necessary, for some other two are needed feo the side of the rotor as viewed bythe reader and weight 32 on the opposite side which is'indicated The group of weights 23', 33',

similarly to the location of weights 23, 30, 3|, 32

in planes a, b, c, d, previously descrlbed,but closer to bearing 3.

The balancing procedure according to` this inf- L vention is based on a removal of a certainportion` of said weights from predetermined planes-a, 5b, l

c, d, and a', b', c', d', by means'` of special stationary removing tools now to be describedin simultaneously. There are,phowever, no balancing operations which require the use of more than two levers at atime,sothat only one opertodescribe now the underlying theory on which. i lil'. is based which will permit a better understanding of its presumed'behaviour.

It is best to conduct this description in three steps:

(A) The description of the performance of the -mechanical part of this invention, i

" Y consisting ina suitable control of removal of weights in the mechanical part of this invention jin accordance with indications exhibited by the j electrical part thereof.

The following description proceeds in the above order.

J In view of the fact that, far as I aware,

fsultantjbalancing forces F' and F" situated in Ythe balancing planes M and Nrespectively. VIironi this well known vtheory ofV balancing. it

follows that a system of balancing forces F' and the principle of Vbalancing on which this invenfV spect/to rotating axes, for the .reasons which will be apparent fromthe following. .I

1 Figure Yirepresents graphically the 'principal vvvectorial relations "characterizing the-dynamics of 'an' unbalanced rotation which can be found in anytextbook of the Applied Mechanics, more jspecinoally in the T i'moshenko book. "Vibration lProblems iny Engineering," 1928. b88es28, 39, 40, 1 fromwhich Figure 4 is taken with slight changes, Y fwith a view to establishing a connection with i the following explanations. Referring 'to Figure r4, the straight line AB represents diagrammati- Ically and in perspective the axis of the rotor I to VVbe balanced; the rotor itself is not shown; the lraxisl AB is shown to besupported by bearings at the points A, B, these bearings corresponding to bearings 2, 3, shown in Figure 1.

' From the theory of balancing it is well known I that the most general case of unbalance can be F" of `a suitable magnitude-and of a suitable angular position intheir respective balancing planes M and N is capable'of neutralizing the disturbing action of the unbalance forces Fraud Fn after which the rotating-'body runs smoothly in its of the balancing procedure.

bearings A and B, which is the ultimate objectA The principal line-of endeavor of practicallyv` yall inventionsrel'ative to the problem of balanc- `ing consists in attempting to determine both the magnitude and the angular location of balancing vector forces F' and F" ln the balancing planesV by observing the maximum deflections and their i tion of balancing weights to be added in the balancing planes M and N is generally determined.

The numerous methods and inventions developedin thisl connectiou'use various means of recording the magnitude and the angular location of the balancing weights to be added in the balancing planes MN which requires the use of either mechanical; electrical, or optical means represented'by two centrifugal forces fixed with respect to the rotor and, hence, rotating with it at the same speed. These forces are shown as lvectors F1 and Fi at right angles to the axis AB of rotation and applied at the points k1 and kn `of this axis: the distance of said points Ici, kz'

from bearings A. B, will be designated by letters ai, b1 and az, bz, respectively. In Ygeneral theV forces Fi and Fn are unequal and non-coplanar,

vmeaning by the last mentioned expression that these forces generally are not contained in the Asame axial'plane passing through the axis of' rotation AB.

Y K- It is well known from the theory of balancing planes M, N.V The location of these balancing planes M. N is arbitrary and is generally selected by considerations' of convenience of each individual problem.

Further, it is also known that a force, say F1,

can be balanced by asystem of two parallel` forces F1'. Fx", situated in balancing planes M. N. respectively, and determined by equations' Similarly the other unbalance force Fn can be Y neutralized by a system of parallel forces F2' and or any combination of these means.

The weak point of all these prior methods lies in the fact that the measurements made by said recording means relate inevitably to displacements of the point at which said measurements of recording is being made and that it is tacitly assumed that the forces causing these displacements are in phase with the latter.

For balancing at low speeds this assumption is approximately correct and the results so obtained are generally satisfactory for practical purposes.

As the speed at which is increased the angular difference between a displacement and the force producing it .becomes more noticeable due to complicated phenomena of damping,l resilience of constraint, gyroscopic phenomena, inertia, damping action of oil films in bearings, and similarfactors. There appears thus a certain appreciable parasitic phase angle between the-displacement and the corresponding force which is commonly called in the balancing practice the phase angle. but which should be called more'properly the parasitic phase angle" Fi" situated also in balancing planesY MN, and

the compensating balancing forces Fi', Fa' and Fr", Fa", being situated in the balancing planes M, N, respectively. can be now combined by the law of the parallelogram of forces into the re- 6000 R. P. M., but there'are no machines, as far as I am aware, capable of balancing at much higher speeds, such as 10,000, 15,000, 20,000 R. P'.- M. or higher, at which some existing rotating machines, such as modern gyroscopes,

operate.

On the other hand, the existing practice of balancing a rotor intended -for anormal operation at high speed (say 20,000 R. P. MJ, at a much lower speed at which it can be balancedA but if it is speeded up to its normal speed of 20,000 R. P. M., an appreciable unbalance will be observed because the same residual unbalance the balancing operation mass at 20,000 R. P. M. will cause unbalance reactions in hearings sixteen times greater than moved upwards and-that associated with tool 35 those which existed at 5000 R. R. M., the centrifu V gal forces increasing in proportion to the square of the angular velocity of rotation.

With these diiiiculties in mind, and cn the f basis of the general theory of balancing outlined in connection with Figure4, I propose now to explain the fundamental feature of the present invention, which, as previously specified, can be designated as the method of balancing with rel spect to therotating axes. The significance of this last mentioned designation will now be explained.

For this purpose assume, to begin with, that the rotor is perfectly balanced initially but that one of the levers of removing tools, for example lever lI3 of the tool 33 shown in Figures 2 and 3 is pushed upwards as indicated by the arrow in Figure 3. As the result of this the abrasive mateopposite (upwards and downwards or vice versa) operation of levers associated with tools 34, 36.

rial 39 will remove a certain portion of the weight 30 rotating in the plane b, which will result in the appearance of a centrifugal vector force Fx. shown in Figure 5, representing the axial view on the section of the rotor, say between the planes a and b. This rotating vectorforce Fx is directed along the diameter of the rotor from its axis 0 towards the weight 29 which is now slightly heavier than the weight 30 because a fraction of the latter has been removed. One can assign arbitrarily to the force Fx lso introduced the sign plus which amounts to defining the positive direction on the diameter passing between the weights 29, 3i), and contained in the same axial plane as the latter, as shown in Figure 5: this diameter becomes thus an oriented rotating axis :c with a definite positive direction on it.

`If, instead of moving the lever 43 of the removing tool 33upwards as iirst considered, said lever were moved downwards, by a similar line of reasoning one can ascertain that this last mentioned procedure would cause the appearance of the force -Fx, directed in the negative direction along the rotating axis x, previously dened. l

By a similar reasoning one observes that by pushing the lever of the removing tool 34 upwards or downwards, the forces -i-Fy or #Fr along a perpendicular rotating axis y can vbe made to appear. The same conclusions are applicable to the other two removing tools 35, 36, but the forces -i-Fx, ,Fia -i-Fy, -Fy brought into play by the operation of these last mentioned tools are confined to the region nearer to the bearing 3, whereas the first mentioned forces i-Fx, -Fx, -i-Fy, -Fy brought 'into play by the operation of levers associated with t0ols`33, 34 are located nearer to the bearing 2. l y

The following conclusions can be formulated from this analysis:

(1) The direction of these various forces Fx, Fy, FX, Fy can be controlled by moving the corresponding levers either upwards or downwards.

(2) The magnitude of said forces depends on the amount of removal of the corresponding weight, that is, on the force with which a corresponding lever is pushed during the removing process as well as on the duration of the latter whichever is more convenient by practical considerations well known to those skilled in the art.

(3) In addition to forces FX, Fy, FX, Fy oriented along the rotating axes .'c, y, as previously considered, the above described method permits introducing the rotating couples as well. For example, if the lever associated with the removing tool 33 is The only dieren'ce in this last mentioned case will be in the fact that the plane of rotating couple so introduced will be at right angles to the couple introduced by the opposite operation of levers associated with tools 33, 35.

One objection can be formulated in connection with the above simple analysis of the method of balancing with respect-to the rotating axes. For

example, assume that the operation of the lever 43 associated with tool 33 is considered. According to whether this lever is pushed either upwards or downwards, either the force +Fx or -Fx is produced as above explained. As far as forces are concerned the analysis is correct; a slight drawbackis seen however in that the plane in .which these forces either -l-Fx or -Fx appear are not exactly the same plane, being separated by :a small distance ro shown in Figure 2. It follows. therefore,-tnat adjustment of forces according to this method is accompanied by a slight disturbing couple having ro as its lever arm.

The above mentioned `drawback is, however, negligible i/n practice for the two reasons- (l) The slight disturbance in the balance of couples so occurring is proportional to the ratio of lengths shown in Figure i2, and can be made negligible bya suitable design. i

(2) The abtual balancing procedure in accord-A ance with this invention deals with the state of unbalance considered as a whole, absorbing both static and dynamic components as felt on both bearings simultaneously, which permits a continuous process of balancing by a rapidly convergent procedure in which all corrections are continuously reduced as will be explained below.

From the foregoing description of the method consisting on varying the forces and couples referred to the rotating axes, the fundamental advantage of this method becomes manifest, In fact, the forces caused by the unbalance are fixed with respect to the rotating system of reference; on the other hand according to the method disclosed Iam able to control the component balancing forces such as Fx, Fy, F'x, Fy, along the rotating axes both in direction and in magnitude; it is thus possible to produce such values of component balancing forces Fx, Fy, F'x, Fy, which will balance exactly the primary unbalance forces F', F". reduced to balancing planes M, N as previously explained in connection with Figure 4. It is also obvious that the above line of argument developed in connection with forces is equally applicable to couples. l

Having. described the mechanical features of this invention, which as previously stated can be designated as the methodof balancing with respect to the rotating axes, I wish to describe now the electrical features thereof as illustrated in Figure 1. These electrical features ultimately result in the appearance of a certain luminous curve on the screen 28 of the cathode ray tube 26 shown in Figure 1. The purpose of the following description is to show how from the size, f orm. and orientation of said luminous'curve and its modification under the eect of balancing with respect to the rotating axes, information guiding the balancing procedure can be obtained.

Following the descriptions and explanations developed in connection with Figure 4, it can be shown that the existence of a general state of unbalance can be analyzed also in the two planes perpendicular to the axis of rotation and passing through the centers of bearings A and B shown in Figure 4, and indicated by numerals 2, 3 in Figure 1. In these planes the rotating reaction applied to the bearings can be represented by two forces, represented as vectors FA and Fn. In the most general case these forces FA and Fa are unequal and non-coplanar; the last designation means that they are contained in two axial planes forming an angle 4 with each other as shown on the right end of Figure 4 at the bearing B.

Y.The components fn and fn of these rotating forces along the vertical stationary axes to which crystals .4 and 5 respectively shown in Figure 1 respond, are therefore of the form:

Where :ma P. M.)

is the angular velocity of rotation in radians per second.

t is the time. (R. P. M.) is the number of revolutions of the shaft per minute.

These alternating vertical forces fa, ,fn applied to crystals 4 and 5 respectively through the well known instrumentality of the piezo-electric effect and the subsequent ampliiication in tubes I2 and I3 adjusted to be the same for both tubes by means of contacts 20, 2l, are iinally represented by two alternating voltages Vx and Vy applied to the deflectng plates 24, 24' .on the one hand and 23, 23' on the other hand.

These voltages can be also expressed by equations of a similar form as Equation 1, that is:

vz=VA cos wt; vy=Vs cos(wt-) (2) The amplitudes VA, Va of these alternating voltages are proportional to forces Fa, Fa previously mentioned. vIt must be noted that the relative phase angle p between the voltages vx and uy is the same as between the rotating vectors FA, Fa.v -In fact, since both the tube channels I2 and I3 are identical, any additional parasitic phase angles that may appear either in the tubes or in the machnical system cancel out and it is the relative phase angle which determines the ultimate shape of the curve on the screen 28 shown in Figure 1.

It is to be noted that the maior difficulty experienced in connection with the absolute determination of the phase angle in the existing balancing machines is eliminated in this invention. In fact, any attempt todetermine the absolute value of the phase angle in the existing machines is handicapped by the existence of an unknown and unpredictable parasitic phase angle appearing partially in the electric lters or other parts of electric circuits and partially in complicated mechanical phenomenaas previously explained.

In case of this invention, however, in view of two identical amplier channels and the identity ofdynamicalconditions associated with bearings A and B, the effect of parasitic phase angles cancels out in both channels and only the relative phase angle is preserved; the'said relative angle is used for guiding the balancing procedure by the shape, size, and orientation of the luminous curve recorded on the screen 28 of the cathode ray tube.

I propose now to establish the equation ofthe luminous curve on the screen 28 which will define its form aswell as its orientation for the variousv cases considered below and to show further how the observations of said form or said orientation of the curve or of its modications permit guiding the balancing operation according to this invention. 4

Since the deflections y, of the luminous spot on the screen 28 are proportional to the voltages, in terms of said deflections, Equation 2 can be written as:

where a: and y designate the deiiections of the luminous spot on the screen along the principal axes :t and y respectively as previously defined and a and are the amplitudes of these deections proportional to the magnitude of forces FA and FB respectively.

The second Equation 3 can be written as:

y= cos (wt-10:5 (cos wt cos+sin wt sin e) whence (1lcos wt coso) sin wt sin (4) Squaring Equation 4 and replacing sin2 wifII--t-:Os2 wt one has:

=2 sin2 (1-cos2 wt) Rearranging the termsof Equation 4a one has:

yz-LZI/ cos wt cos qb-i-z cos2 wtz sin2 (4b) In this last equation cos wt can be expressed from the iirst Equation 3, namely:

Substituting forcos wt its value in Equation 4b one obtains after the reduction to a common denominator 2 which is dropped thereafter, the following expression:

Equation 5 is the basic equation and will be now discussed. Before considering however the general case represented by Equation 5, it is useful for the following to study a series of particular `cases which will permit establishing a relation The fact that =0 physically means that the rotating forces FA, Fa shown in Figure 4 are coplanar; in other words, in this case one has a `if the angles are measured in radians purely static unblance, shown in Equation becomes in-this case:

(ay-pneu that is Ly-cmo Figure 6B.

t Otherwise' written it is:

Equation 5,1 represents a straight line situated in the rst quadrant defined by positive directions of axes and y, passing through the origin and having the slope y defined by equation:

slope is indicative of its position along the axis of rotation. If the static unbalance force F approaches the bearing A, which is indicated as 2 on Figure 1, the luminous line turns towards the :r axis, which is shown' by arrow on Figure 6A; if this force approaches B `(that is bearing 3 on Figure 1) it rotates in the opposite direction.

The luminous line D cannot penetrate, however, in th'e case of a purely static unbalance, into the shaded region shown in Figure 6A, because the resultant unbalance force cannot occur to the left of the point Km or. to the right of the point 'Kao shown in Figure 6B corresponding to the terminal plane 44, i5 of the rotor, as shown in Figure 1. These limit inclinations 7172 ot the luminous line can be determined experimentally dur ing la preliminary calibration of the balancing machine by attaching to a perfectly balanced rotor, rst a weight in the plane 44. After determining by this procedure the angle 71, a similar preliminary calibration is reproduced by attaching a weight in the plane 45, which determines th'e other limit slope Y2 shown in Figure 6A. It can also be calculated without said preliminary calibration. Conversely if, after these preliminary calibrations, it is observed` that the luminous straight line D is situated in the non-shaded sector shown in Figure 6A, this will be indicative of the facts that- (a) The imbalance forces are coplanar. (b) That this static unbalance either exists in its pure form, or that it exists in conjunction with the dynamic unbalance, as will be explained in the third case below.

Second case, a pure dynamic unbalance. In

` this case the unbalance reactions FA, Fs applied to bearings A, B are always equal and opposite as shown in Figure 7A, while still being coplanar. This results from the definition of the couple; in fact for a purely dynamic unbalance there is no resultant force present. form in this case a couple, which is balanced also by a couple of reaction in bearings which results in the presence of equal and opposite reaction forces Fs, FB shown in Figure 7B, applied to bearings A and B, said forces being also coplanar. The relative phase angle e in this case is 180, or 1r Putting =1r in Equation 5, which results in and putting also a= for the above mentioned reason, one obtains iinally:

This is an equation-,of a straight line D shown in Figure 7A and inclined under the angle fy=135 f with respect to the positive direction of the a: axis as shown. There is no direction other than possible 1r the unbalance is purely dynamic. The` experimental procedure of balancing becomes very simple as will be later explained.

Third case, simultaneous presence of pure static h and pure dynamic coplanar unbalances. This case is shown in Figure 8B, in which Fs is th'e resultant force of the static unbalance. giving rise to copianar reactions FA, Fs; and FF is a coplanar dynamic'unbalance couple having lever arm n. The corresponding reactions in the bearings are F'A and F'B. It is seen from Figure 8B that in this case under certain particular conditions easily ascertained by an elementary calculation omitted here, the effect of corresponding static and dynamic reactions may cancel out in one of the bearings, For the position oit the resultant force FB of the static unbalance and of the couple E'F' ofthe dynamic unbalancle shown, it is seen from an oil-hand consideration that this cancelling out may occur at the bearing B.

When this condition exists, the bearing B becomes a center of percussion. In such' a case the shaft runs smoothly in bearing B, but the hammering continues in bearing A under the jointieiect of reactions FA, F'A. Since no alternating forces are applied in this casein bearing B, the alternating voltage resulting from the 'alternating forces applied to crystal 5, shown in Figure 1, disappears and, hence the vertical motion of the luminous spot on the screen 28 ceases. The motion of the luminous spot is then confined to the axis, as shown in Figure 8A. If the center of percussion would occur in the other bearing A, by a. similar line of argument one concludes that the luminous` line D', shown in Figure 8A would coincide with the y axis on the screen.

Conversely if it is observed that the luminous line D (or D) coincides with one of the principal axes .'c, y of the screen of the cathode ray tube 26,

a conclusion can be derived from this fact that the corresponding bearing becomes a center of The dynamic reactions percussion. More specifically, if the luminous line coincides withthe :c axis, the bearing Bis the center of percussion;` if it coincides with the 1/ axis, the bearingA is the center of percussion.

Having ascertained all possible cases of a pure static and a pure dynamic unbalance as well as of their copolanar combination with respect to the corresponding luminous record observed on vthe screen of the cathode ray oscilloscope arranged to respond to the unbalance forces in the above described manner, I wish to analyze now the eiect of non-copolanar unbalanceforces on rthe luminous image observed on said screen.

Fourth case. Before analyzing the most general case when the reactions in bearings are unequal and form any angle e, which is repref 15 i sented mathematically by Equation 5, I wish to describe first an additional particular case when 5 shown diagrammatically in Figure 9B. Referring to Equation 5 in which Lg-f1 This equation represents an ellipse referred to the principal axes z, y. On the screen 28 of the cathode ray oscillograph the luminous curve will Y be then an'ellipse referred to the principal axes x, y of the screen and shown as curve D in Figure 9A. This curve D presupposes that the unbalance reaction FA in bearing A is greater ,than the corresponding reaction FB in bearing B. If, on the contrary the reaction FB- is greater than FA, the luminous ellipse has the form D' shown in Figure 9A. If the rotating reaction forces Fx and FB happen to be equal, the ellipse reduces itself to a circle D".

`It is to be noted also that in case the vector force Fa shown in Figure 9B is oppositely directed as shown in dotted lines, angle in this case is 270, or

if measured in radians. The other reaction FA remaining the same, the luminous elliptic cur-ve in this case would be exactly the same as in the above described case when all other factors remaining the same.

Having described these various particular cases, the general case mathematically represented by Equation 5 rwill now be analyzed.

As is -well known from analytical geometry (e. g. see @textbook by C. Smith, entitled Conic sections; Coordinate Geometry, Chapter IX) Equation 5 represents an ellipse E, not referred to the principal axes, as shown in Figures 10A and 10C corresponding to the state of unbalance shown diagrammatically in Figure 10B. In this last mentioned gure, angle p may have any value except the values i In order to abbreviate the following description, I propose to use a, conventional language, the signiiicance of which will be apparent from the following. Referring to Figure 2 showing the arrangement of removing tools 33, 34, 35, 36 in their relative position with respect to the rotor to be balanced, I will designate as operation (i: 33), an operation in which the lever 43 of the removing tool 33 is moved upwards as shown by arrow in Figure ,3, which results in the removal of material from the balancing weight situated in plane b and in. the corresponding production of the balancing force i Fx directed along the positive direction of the rotating axis :c shown in Figure 5. Accordingly by operation (-33) will be designated the case when saidy lever 43 is moved downwards which results in the removal of material from the weight 2 9 located in plane a, shown I'with the consequent production of the balanc-v ing force -Fx directed along the negative direction of said :c axis. Likewise operations (-34) and (+34) will result in the removal of material from balancing weights 3| and 32 situated respectively in planes c and d with the consequent appearance of balancingV components of forces +Fy and -Fy directed along the perpendicular rotating axis y.

previously considered in connection withl the above described four particular cases, which, for that reason, will be now excluded.

In-practice this general case'will be practically the .only one to be considered at the beginning of the balancing operation. While there is no diiiiculty in establishing additional relations connecting the form as well as the orientation of axes of the luminous ellipse observed on the screen in this general case with respect to the principal axes y on that screen, there is no further advantage in proceeding in this direction because the general method of balancing according to this `invention can be .now ascertained. l

Operations (+35), (F35), (+36), (-36) 'will be similarly denedwith respect to the removing tools 35, 36, balancing weights 29', 30', 3|', 32 and the corresponding balancing forces +F/x, -Fx, +F'y, -F'y not shown but similarly directed as the rst mentioned non-primed balancing forces but situated nearer the bearing 3.

The conventional terminology so defined is convenient inasmuch as it permits reducing long sentences to the above symbolic expressions. Thus, for example, according to this convention, an operation (+33, +35) will result in the introductio'n of coplanar balancing forces +Fx, +Fx in the previous notations; an operation (+33, -35) will result in the production of a force +Fx near/the bearing 2 and of a corresponding force -F near the bearing 3, which will result accordingly in the appearance of a rotating couple situated in the rotating axial plane dened by the rotating axis :r or likewise an operation (-33, +35) will result in the' appearance of a similar couple located inthe same plane zo." but having lan opposite direction.

Similarly operations (+34, +36) or (-34, -35) will result in the appearance o f coplanarbalancing reactions directed respectively along either positive or negative direction of the rotating y, y' axes. 'Likewiseoperations (+34, -36) or (-34,

+36) will cause the production of balancing roforces F1, F2 as well as their components in the various planes such as planes a, b, cpd, a', b', c', d', remain fixed.

This permits obtaining rapidly a state of nal perfect balance in one single continuous balancing procedure applicable to balancing at any speed however high. This valso permits obviating the great diiiiculties incident to the existence of a parasitic phase angle, inherent in the existing balancing machines.

In order toshow how the balancing operation is performed with the balancing machine forming the object of this invention, assume that at the beginning of the balancing the luminous curve observed on the screen 23 of the cathode ray oscillograpl has the form shown in Figure A, 'evidencing the existence of unequal and non-coplanar rotating reactions FA and Fa in bearings died out, which will take a short time, say, a second or so. Two cases are possible:

(l) The original ,ellipse becomes -wider ap- .V proaching the circle.

(2) It becomes narrower, approaching a straight line.

- Assume 'the latter condition: one can again apply' the operation (+33) or if one wishes to avoid the excessive removal of material from the same balancing weight one can try the operation which gives rise to a balancing force coplanar with that which is caused by the operation (+33).

As the -result of these `operations the original ellipse D will become more elongated and narrower as shown by curve D"in Figure 10A. It'

' angle Y, which will become now ly' after said ilrst trial operation. The above described procedure Y of narrowing the ellipse from the form D to the form D' physically means that the-state of the balance gradually approaches that of a purely static unbalance when the ellipse degenerates finally into a straight line Do as was investigated in the iirst particular case for =0 and illustrated in Figure 6A.' When this last mentioned condition is reached a purely static unbalance exists, as shown in Figure 6B. As soon as this point is reached during the balancing operation', the subsequent operation will be either (+33, +35) or (-33, -35) whichever gives the reduction of length of the luminous straight line Do. .,If both these` operations fail to cause an ap- 1 preciable changezof lthe length of the line D, this ffact will indicate` that the balancing forces introduced by the removalof material (such asy +Fx, +F'x or -Fx, -F'x) are substantially at right anglesto the unbalance reactions FA, Fe in bearings A and B respectively. In such a case an alternative operation` (+34, +36) or (-34, -38) should be tried; .oneoi these operations will certainly cause agradual reduction of the length of line Do and this' particular combination of oper- Y ations must be continued until the line Do shrinks to one point, whlchis the criterion of a perfect balance in both bearings A and B.

There may be another possibility when the ellips@ initially has a form shown in Figure 10c.-

By making a fewvtrialelementary operations such as (+33), (-33) (+34), (-34) etc. one can easangle formed by the negative diigections o! the principal axes on the screen 28. When this condition is reached there is an evidence that the initial unbalance by means ofthe above described preliminary operations has been reduced to a pure dynamic unbalance as described in the. second particular case =1r=180 and illustrated'in Figures '7A and 7B. As soon as this stage of the balchangeof the length of line D, this indicates that i the plane of the balancing couple sointroduced is at right angles to the plane of the couple causing the dynamic unbalance. In such a case a1- ternative combinations will be (+34, -3-3) (-34, +38); one of these causing a reduction oi.' the length oi the luminous line Do must be continued until this line shrinks to one point which indicates again the state of a perfect balance.

The above disclosed procedure of balancing withrespect to the rotating axes determined by the diameters in the plane of the weights 23. 33, (29', 30') on the one hand and the diameters in the plane of weights 3l, 32, (3l', 32') on the other hand guided by theshape as well as by the orientation of luminous curves on the screen 28, as above described, is quite general and capable of a number of other` experimental procedures.`

Thus for example, instead of proceeding along the line oiv a gradual narrowing of` the original luminous ellipse D shown in Figures 10A and 10C. the balancing procedure may follow an opposite course, that is'that of a gradual wideningv of said ellipse through the instrumentality of preliminary trial operations as above described.

Assume, for instance, that the-preliminary trial operation results in a widening of the ellpise with the incidental change of the angle ybetween the axis of the ellipse and the'principal axis X of the oscillographic screen. Continulngthis operation, a state of the balance wilLbe eventually reached when the luminous ellipse will appear as referred to the principal axes on the screen, as shown in It is thus seen thaty the number ofl different procedures by whlchfthe balancing procedure can be best carried out is considerable and that a skilled operator can rapidly guidethe balancing operation to the state of a perfect balance.' VIn such as ellipse D", shown inFigure 10C. In such a case the operation should be continued until the ellipse graduallyfdegenerates into a straight line Do, `which inthislcase'will be a Iinebisecting the selectingone or the" other procedurethe'following general rules must be kept in mind.

(a) A balancing operation 'carried out by means of operations such as'(i33) or. (2:34) changes obviously the reaction force FA in bearing 2 shown in Figure 1 to a greater extent than that in -bearingll because said removingtools 3 3.

34, are nearer to bearing 2 than tothe bearing. Conversely. balanciusfbperations; (#35).; (nu) modify more the reactions in bearing! than in Y of the same sign, which is apparent from the previous discussions relative to the decommsition oi' `a force into two parallel components. (c) A balancing operation, upon the reduction of the general state of unbalance to a purely dynamic form shown in Figures 7A and 7B, requires a combination of operations (+33) (-35) (-33) (+86); or (+34) (-38): (-M) (+36) of opposite signs, which is also apparent inasmuch as such'operations introduce rotating couples as previously shown. f

(d) A balancing operation, upon the reduction of the general state of unbalance to the quadrature (=90) reactions as .shown in Figures 9A and 9B, requires a combination of operations (in), ($36), or (i3d), ($35) because these aiiect quadrature components in both bearings.

(e) If one balancing operation does -not vproduce an appreciable change in the luminous image on the screen, a combination introducing balancing forces at right angles to those previously tried will certainly produce such a reduction leading to a balancing procedure rapidly converging towards the state of aiinal perfect balance.

(f) Balancing combinations of the type described will always result eventually in a. nal state oi.' a perfect balance because being given any' arbitrary unbalance vector force FA or FB I Y stationary with respect to the rotating axes a', '11,

. shown in Figure and contained in the axial ysis relative to the performance of the balancing machine forming the subject of this invention, it

can'be statedl that the approach to the state of a perfect balance is carried out according to this v inventionby a continuous procedure and by a rapidly convergent sequence of Vbalancing operay tions, each succeeding operation improving and correcting the results obtained by the preceding operation. These balancing operations are guided bythe prevailing state ofthe total unbalance existing in both bearings simultaneously and exhibited by the form, size, and orientation relative to the principal axes on the screen of luminous curve characterizing said state of total un- -f balance in the above decsribed manner.

Although, as previously stated, the balancing machine of the type described can be adapted both for low speed rotors and for high speed rotors, its advantages are particularly marked for ofbalancing weights requires stopping the rotor of this invention, the rotor will be balanced grad' uaily when the speed is yet relatively small, the

initial avoirdupois unbalance great, and the cen-V trifugal reactions in bearings relatively 'moderate due to said small speed. As the speed increases and the balancing procedure continuing from time to time, say, every minute or so, the avoirdupois unbalance removed each time decreases but the effect of this residual unbalance increases due to the increasing speed, in proportion to the square of the latter. If the rotor happens to pass through a series of critical speeds, the balancing operation must be momentarily discontinued during such periods of critical speeds and resumed thereafter. Vwhen the critical speed has been passed.

As the speed increases the removal of material by tools 33, 34, 35, 36, required for balancing becomes smaller andsmaller and the changes in the shape as well as in the orientation oi the luminous curve on the screen in response to the slightest touches of the abrasive material from the rapidly rotating balancing weights becomes more and more pronounced. f

The balancing operation is thus conducted progressively in a continuous manner and by the time that the rotor reaches its Vnal 'high speed of normal operation, it will be thus perfectly balanced. i

From the above discussion it follows that in addition to the above mentioned advantage of` nishing the balancing operation by a continuous procedure by the time the rotor reaches its normal speed, this invention offers an additional advantage by providing conditions by which the balancing operation is `effected at substantially constant centrifugal reactions in vthe bearings and, hence, in the piezo-electricelements 4, 5,

as well as in the voltages transmitted through the very high speed rotating machinery such as modi ern Vgyroscopes, for which there'exist no methods of obtaining a rapid and continuous balancing at the full rated speed of their rotation.

The existing methods require a long and painstaking procedure of balancing at considerably lower speeds than that for which these rotors are normally intended. Each subsequent adjustment tubes i2, i3, s hown in Figurel. This last mentioned advantage is particularly important from the standpoint of the engineeringdesign of the pressure responsive elements l, 5, as well as the amplifying systems. Furthermore, it permits reducing the amount of adjustments by means ofV the connection 22 shown in Figure 1 to a minimum, as the balancing operation goes through its subsequent stages.

Although I have describedv a particular embodiment of this invention, I wish it to be understood that many modicationsrand changes in said embodiment arepossible'without any departure from the scope of this invention as defined in the following claims.

Having thus-described the invention, what is claimed as new and desired to be secured by Letters Patent is:

1. In an apparatus for indicating the state o! unbalance of a rotor, bearings supporting said rotor at points spaced axially thereof, means for rotating said rotor, a piezo-electric system associated with each of said bearings, an amplifier' system comprising two amplifier channels one connected with each of said piezo-electric systems, said amplifier systems serving to amplify the alternating voltages generated in said piezoelectric systems by the forces of unbalance at said respective bearings, a cathode ray tube, and means connecting thc respective pairs of deilecting plates of said tube with said amplifying systems whereby a luminous curve is produced on the screen of said tube which is indicative of the state of unbalance at both of said bearings.

2. In an apparatus for indicating the state of unbalance of a rotor, bearings supporting said rotor at points spaced axially thereof, means for rotating said rotor, `a piezo-electric system associated with each of said bearings, an amplifier system comprising two amplifier channels one connected ,with each of said piezo-electric systems, said amplifier systems serving to amplify the alternating voltages generated in said piezoelectric systems by the forces of unbalance at said respective bearings, means for adjusting the amplication factor of each of said channels, means for adjusting the amplification ratio of both channels simultaneously by equal amount, and a prises supporting said rotor at axially spaced points, ailixing weights to said rotor at points spaced from the axis and in a plurality of differ-- ent planes which include the axis of rotation, rotating said rotor, obtaining a piezo-voltage at each of said points of support proportional to the pressure reactions due to unbalance at said points, amplifying said voltages and converting them into a combined visual image which exhibits cathode ray tube having two pairs of deflecting both the magnitudes and directions of said forces, and selectively removing portions of said weights during rotation, and in accordance with said indication untilvsaid image narrows to a point. which corresponds to a state of balance of the rotor, all without interrupting the rotation thereof.

NICOLAI MINORSKY.

REFERENCES CITED The following references are of record in the le of this patent: v

UNITED STATES PATENTS 

